CURVED.IT: A design tool to integrate making with curved folding into digital design process

The act of changing the direction of a sheet surface along a non-straight curve is a specific case of curved folding. From an architectural point of view, curved folding is an exciting operation. One or a couple of operation can generate highly complex shell-like spatial enclosure. From a digital design perspective, the imple-mentation of curved folding with the built-in toolsets of available computer-aided design softwares is a challenging problem. The equilibrium state of curved folded geometry is needed to be found with a computational form-finding strategy. To use curved folding as a digital design operation, we introduce a new tool through developing a digital procedure for form-finding. The tool we develop can enable the experimentation with curved folding in the early stage of design process and facilitate the subsequent design development. In this article, we briefly present the literature focusing on curved folding in computational geometry, as well as the scope and description of a subclass of curved folding operation. Then, we intro-duce a digital tool, CURVED.IT through a design manual for its implementation and an algorithmic framework for its extension. Lastly, we discuss the design ex-amples generated by CURVED.IT, and the potentials of the tool.

___

ACI Committee, American Concrete Institute, & International Organization for Standardization. (2008). Building code requirements for structural concrete (ACI 318-08) and commentary. American Concrete Institute.

Architects, P. (2017). Patkau Architects: Material Operations. Princeton Architectural Press.

Barnes, M. R. (1977). Form finding and analysis of tension space structures by dynamic relaxation (Doctoral dissertation, City University London).

Brancart, S., Vergauwen, A., Roovers, K., Van Den Bremt, D., De Laet, L., & De Temmerman, N. (2015). UNDULATUS: design and fabrication of a self-interlocking modular shell structure based on curved-line folding. In Future visions; Proc. intern. symp., Amsterdam, 17-20 August 2015.

Bhooshan, S., Bhooshan, V., ElSayed, M., Chandra, S., Richens, P., & Shepherd, P. (2015). Applying dynamic relaxation techniques to form-find and manufacture curve-crease folded panels. Simulation, 91(9), 773-786.

Bollinger, K., Bollinger, K., Grohmann, M., & Schmal, P. C. (2004). Workflow: Struktur-Architektur. Brikhäuser.

Burry, M. (2011). Scripting cultures: Architectural design and programming. John Wiley & Sons.

Chandra, S., Körner, A., Koronaki, A., Spiteri, R., Amin, R., Kowli, S., & Weinstock, M. (2015, April). Computing curved-folded tessellations through straight-folding approximation. In Proceedings of the Symposium on Simulation for Architecture & Urban Design (pp. 152-159). Society for Computer Simulation International.

Day, A. S. (1965). An introduction to dynamic relaxation(Dynamic relaxation method for structural analysis, using computer to calculate internal forces following development from initially unloaded state). the engineer, 219, 218-221.

Dias, M. A., Dudte, L. H., Mahadevan, L., & Santangelo, C. D. (2012). Geometric mechanics of curved crease origami. Physical review letters, 109(11), 114301.

Duncan, J. P., & Duncan, J. L. (1982). Folded developables. Proc. R. Soc. Lond. A, 383(1784), 191-205.

Epps, G., & Verma, S. (2013). Curved Folding: Design to fabrication process of RoboFold. Shape Modeling International 2013, 75.

Eversmann, P., Ehret, P., & Ihde, A. (2017). ’Curved-folding of thin aluminium plates: towards structural multipanel shells’. Proceedings of the International Association for Shell and Spatial Structures.

Fuchs, D., & Tabachnikov, S. (1999). More on paper folding. The American Mathematical Monthly, 106(1), 27-35.

Geretschläger, R. (2009). Folding Curves. In Origami 4, Lang, R. J. (Ed.). CRC Press, 151.

Huffman, D. A. (1976). Curvature and creases: A primer on paper. IEEE Transactions on computers, (10), 1010- 1019.

Kilian, M., Flöry, S., Chen, Z., Mitra, N. J., Sheffer, A., & Pottmann, H. (2008). Curved folding. ACM transactions on graphics (TOG), 27(3), 75.

Kilian, A., & Ochsendorf, J. (2005). Particle-spring systems for structural form finding. Journal of the international association for shell and spatial structures, 46(2), 77-84.

Koschitz, D., Demaine, E. D., & Demaine, M. L. (2008). Curved Crease Origami, Proceedings of the Advances in Architectural Geometry, Vienna, Austria, Sept, 29-32.

Lalvani Haresh, 2003.

URL: http://www.metropolismag. com/uncategorized/bend-the-rulesof-structure/

Lamere, J., Gunadi, C. (2011). Overliner.

URL: http://www.gldarch.com/ projects/show?utf8=✓&tag=16&project=3

Lee, T. U., You, Z., & Gattas, J. M. (2018). Elastica surface generation of curved-crease origami. International Journal of Solids and Structures.

Mitani, J and Igarashi T. (2011). Interactive Design of Planar Curved Folding by Reflection. In: the 19th Pacific conference on computer graphics and applications. Kaohsiung, Taiwan: Pacific Graphics.

Pottmann, H. (2007). Architectural geometry (Vol. 10). Bentley Institute Press.

Resch, R. D. (1974). The Space Curve as a Folded Edge. In Computer Aided Geometric Design (pp. 255-258).

Scheurer, F., Schindler, C., & Braach, M. (2005). From design to production: Three complex structures materialised in wood. In 6th International Conference Generative Art.

Scott, C., & Iwamoto, L. (2012). Voussoir Cloud. In Matter: Material Processes in Architectural Production (pp. 68-80). Routledge.

Sutherland, I. (1963). SKETCHPAD-a man-machine graphical interface (Doctoral dissertation, PhD thesis, MIT).

Tachi, T., & Epps, G. (2011, March). Designing One-DOF mechanisms for architecture by rationalizing curved folding. In International Symposium on Algorithmic Design for Architecture and Urban Design (ALGODE-AIJ). Tokyo.

Vergauwen, A., De Temmerman, N., & De Laet, L. (2014). Digital modelling of deployable structures based on curved-line folding. In Proceedings of the IASS-SLTE 2014 Symposium “Shells, Membran and Spatial Structures: Footprints.

Vergauwen, A., De Laet, L., & De Temmerman, N. (2017). Computational modelling methods for pliable structures based on curved-line folding. Computer-Aided Design, 83, 51-63.

Williams, C. J. (2001). The analytic and numerical definition of the geometry of the British Museum Great Court

Roof. Williams, C. (2014). What is a shell. Shell structures for architecture: form finding and optimization, 21-31.